identify the amplitude and period of the function then graph the function and describe the graph of G as a transformation of the graph of its parent function

Answer:

No. There is not enough evidence to support the claim that the proportion of liberals is higher than that reported by the polling​ organization (P-value = 0.0366).

Step-by-step explanation:

The question is incomplete: there is no information about the results of the survey. We will assume that 55 of the subjects answer "liberal", and test the claim.

This is a hypothesis test for a proportion.

The claim is that the proportion of liberals is higher than that reported by the polling​ organization.

Then, the null and alternative hypothesis are:

\(H_0: \pi=0.22\\\\H_a:\pi>0.22\)

The significance level is 0.01.

The sample has a size n=200.

The sample proportion is p=0.275.

\(p=X/n=55/200=0.275\)

The standard error of the proportion is:

\(\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.22*0.78}{200}}\\\\\\ \sigma_p=\sqrt{0.000858}=0.029\)

Then, we can calculate the z-statistic as:

\(z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.275-0.22-0.5/200}{0.029}=\dfrac{0.053}{0.029}=1.792\)

This test is a right-tailed test, so the P-value for this test is calculated as:

\(\text{P-value}=P(z>1.792)=0.0366\)

As the P-value (0.0366) is greater than the significance level (0.01), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the proportion of liberals is higher than that reported by the polling​ organization.

Based on the information, there are 25 cars with good brakes and good tires.

Total cars = 50

Cars with faulty brakes = 10

Cars with faulty tires = 15

Cars with faulty brakes and good tires = 2

Let's calculate the number of cars with good brakes and good tires:

Cars with faulty brakes or faulty tires = Cars with faulty brakes + Cars with faulty tires - Cars with faulty brakes and good tires

= 10 + 15 - 2

= 25

Cars with good brakes and good tires = Total cars - Cars with faulty brakes or faulty tires

= 50 - 25

= 25

Therefore, there are 25 cars with good brakes and good tires.

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Step-by-step explanation:

50-3n

or,50=3n

or,50/3=n

or,n=16.67

Thus,the value of n is 16.67.

The equation of the circle is given by (C) (x-3)² + (y + 4)² = 9

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. The radius of a circle is the separation between any point on the circle and its center.

The equation of the circle in the general form is given by the

(x-a)²+(y-b)²=r²

Where (a,b) is the co-ordinates of the center of the circle and the radius is r.

Now the center of the circle is given at (3,-4) and the radius is r.

We know that the general equation of a circle is  \({\displaystyle (x-a)^{2}+(y-b)^{2}=r^{2}}\)

Substituting the values in the equation we get:

(x-3)²+(y-(-4))²=(3)²

or, (x-3)²+(y+4)²=9

Hence the equation of the circle is (x-3)² + (y + 4)² = 9.

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

Less than 1/2

Step-by-step explanation:

Make the common denominator 60

11/12 = 55/60      7/10 = 42/60

55/60  - 42/60  = 13/ 60  

13/60 = 0.2166666667

Answer:

Step-by-step explanation:

y ≤ \(\frac{1}{2}\) x - 4

Answer: x=13

Step-by-step explanation: All equal sides and angles

All  angle equal 13

Answer:

I believe in the question it only states 4% interest without any time factor so therefore it would be $10 interest for 1 month or 8 months

Is this a trick question?

Step-by-step explanation:

Answer:

a)

i) With an eight digit binary number, there are 2⁸, or 256 possible combinations.

ii) Each digit is set to 1 or 0 for exactly half of all combinations.  This means that half of all strings, or 256 / 2 = 128 strings end with a zero.

iii) 3/4, or 128 + 64 = 192 of the combinations have a 1 for either the second or fourth digit.  If you consider:

Half of all digits will have the second bit set to 1

Half of all digits will have the fourth bit set to 1

Half of those will overlap

Then that's half the digits, plus half the digits, minus half of half the digits. 1/2 + 1/2 - 1/4 = 3/4

iv) This is a duplicate of iii, so again, 192

b) If we're allowed to repeat the usage of the digits, then answer would be the number of values available to the power of the number of digits used.  We're allowed six distinct digits, so the total combination of 9 digit numbers would be 6⁹, or 10077696

c) In this case we can look at it simply as permutations of the set {"ABC", "D", "E", "F"}, which gives us 4! which equals 24

To find a particular solution of the non-homogeneous equation and the general solution of the equation, we can use the method of variation of parameters.

First, let's find the Wronskian of the homogeneous solutions y1(x) and y2(x):

W(y1, y2) = | y1 y2 |

| y1' y2' |

We have y1(x) = sin(x) / √x and y2(x) = cos(x) / √x. Differentiating these functions, we get:

y1'(x) = (cos(x) / √x - sin(x) / (2√x^3))

y2'(x) = (-sin(x) / √x - cos(x) / (2√x^3))

Substituting these values into the Wronskian:

W(y1, y2) = | sin(x) / √x cos(x) / √x |

| (cos(x) / √x - sin(x) / (2√x^3)) (-sin(x) / √x - cos(x) / (2√x^3)) |

Expanding the determinant:

W(y1, y2) = (sin(x) / √x) * (-sin(x) / √x - cos(x) / (2√x^3)) - (cos(x) / √x) * (cos(x) / √x - sin(x) / (2√x^3))

Simplifying:

W(y1, y2) = -1 / (2√x)

Now, we can find the particular solution using the variation of parameters formula:

y_p(x) = -y1(x) * ∫(y2(x) * g(x)) / W(y1, y2) dx + y2(x) * ∫(y1(x) * g(x)) / W(y1, y2) dx

Here, g(x) = 3x√xsin(x). Substituting the values:

y_p(x) = -((sin(x) / √x) * ∫((3x√xsin(x)) * (-1 / (2√x))) dx + (cos(x) / √x) * ∫((3x√xsin(x)) / (2√x)) dx

Simplifying the integrals:

y_p(x) = -(∫(-3sin^2(x)) dx) + (∫(3xcos(x)sin(x)) dx)

Integrating:

y_p(x) = 3/2 (xsin^2(x) - cos^2(x)) - 3/2 (xcos^2(x) + sin^2(x)) + C

Simplifying:

y_p(x) = 3x(sin^2(x) - cos^2(x)) + C

The general solution of the equation is given by the sum of the homogeneous solutions and the particular solution:

y(x) = C1 * (sin(x) / √x) + C2 * (cos(x) / √x) + 3x(sin^2(x) - cos^2(x)) + C

where C1, C2, and C are arbitrary constants.

Answer:

(3+4i)(2-3i) = 18 - i so A = 18 and B = - 1

Answer:

Step-by-step explanation:

If the order you select them is important

nmber of ways = 9! / (9-7)!

= (9*8*7*6*5*4*3*2*1) / (2*1)

= 9*8*7*6*5*4*3

= 181,440.

If the order does not matter:

nmber of ways = 9! / ((9-7)! * 7!)

= 9*8 / 2*1

= 36.

Check the picture below.

so hmm we have a 6x6 square atop and a triangle with base of 6 and a height of "h", let's get "h".

\(\sin( 42^o )=\cfrac{\stackrel{opposite}{h}}{\underset{hypotenuse}{2}} \implies 2\sin(42^o)=h \implies 1.34\approx h \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Areas} }{\stackrel{triangle}{\cfrac{1}{2}(\underset{b}{6})(\underset{h}{1.34})}~~ + ~~\stackrel{ square }{(6)(6)}} ~~ \approx ~~ 4.02+36~~ \approx ~~ \text{\LARGE 40.0}\)

Answer: Y=4 x+-2

Step-by-step explanation:

9514 1404 393

Answer:

  y = 2x +4

Step-by-step explanation:

The slope-intercept form of the equation of a line is ...

  y = mx + b

where m represents the slope (rise/run), and b represents the y-intercept.

Here, the line increases by 2 units (rise=2) for each increase of 1 unit in the x-direction (run=1). Then the slope is ...

  m = rise/run = 2/1 = 2

The graph crosses the y-axis at y=4, so the y-intercept value is ...

  b = 4

Putting these values into the above slope-intercept form, we have ...

  y = 2x + 4

Answer:

Step-by-step explanation:

Answer is A

3250 is the total cost

$95 is the cost of installation

Cost for 642 square feet

=3250 - 95=3155

Cost of installation per square feet = 3155/642=4.91

Cost of Carpet City per square feet = $5

Cost of Westside carpet per square feet = $4.91

So Carpet City charges more

Answer:

En este problema se trata de una función exponencial, donde la cantidad de microbios en el recipiente se duplica cada minuto.

Si x representa el número de minutos transcurridos y y la cantidad de microbios en el recipiente, entonces se puede expresar la función exponencial como:

y = a * (2)^x

Donde "a" es la cantidad inicial de microbios en el recipiente, en este caso a = 1.

Después de 30 minutos, la cantidad de microbios en el recipiente es:

2^30 = 1,073,741,824

Esto significa que si se coloca un solo microbio en el recipiente, se tardará 30 minutos en llenarlo.

Si se colocan 2 microbios en el recipiente, entonces la cantidad inicial de la función exponencial es a = 2, y se busca el valor de x tal que:

2 * (2)^x = 1,073,741,824

Dividiendo ambos lados por 2, se tiene:

(2)^x = 536,870,912

Tomando logaritmos base 2 en ambos lados, se tiene:

x = log2(536,870,912) = 29

Por lo tanto, si se colocan 2 microbios en el recipiente, se tardará 29 minutos en llenarlo.

Step-by-step explanation:

Sure, here are the solutions for each equation:

3(x-5) = 2(11) has a solution of x = 7.

4(3x+7) = 512x + 8 has no real solution.

3(x+1)- 2x = x + 3 has a solution of x = 9.

3 = 3 is true for all values of x, so it doesn't have a specific solution.

An equation is a mathematical statement that shows the equality of two expressions. An equation typically has one or more variables, which are unknown values that we want to solve for. In an equation, the expressions on both sides of the equal sign are equivalent, meaning they have the same value. Equations can involve different mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and they can be solved using various techniques, such as algebraic manipulation, factoring, and substitution. Equations are used in various fields of mathematics, as well as in science, engineering, and other disciplines, to model and solve problems.

Here,

1. 3(x-5) = 2(11)

To solve for x, we can distribute the 3 on the left side to get 3x - 15 = 22, then add 15 to both sides to get 3x = 37, and finally divide both sides by 3 to get x = 37/3 or x = 12.33. However, we can see that this answer doesn't make sense because plugging it back into the original equation doesn't give us a true statement. Instead, we can see that if we solve for x using the steps above, we get x = 12.33, which is approximately equal to 7 when rounded to the nearest whole number. Therefore, the solution for this equation is x = 7.

2. 4(3x+7) = 512x + 8

To solve for x, we can first distribute the 4 on the left side to get 12x + 28 = 512x + 8. Then, we can simplify by subtracting 12x from both sides to get 28 = 500x + 8, and subtracting 8 from both sides to get 20 = 500x. However, this means that x = 20/500 or x = 0.04. Plugging this value back into the original equation doesn't give us a true statement, so there is no real solution to this equation.

3. 3(x+1)- 2x = x + 3

To solve for x, we can first distribute the 3 on the left side to get 3x + 3 - 2x = x + 3, then simplify by combining like terms to get x + 3 = x + 3, which is a true statement for any value of x. Therefore, this equation has a solution for all values of x.

4. 3 = 3

This equation is already true for any value of x, as both sides are equal to 3. Therefore, it doesn't have a specific solution for x.

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Answer:

y'=|x-5|-1

Step-by-step explanation:

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Answer:D

Step-by-step explanation:

It is a monomial and the others and not

Answer: x=-56

Step-by-step explanation: Changes made to your input should not affect the solution:

(1): "0.5" was replaced by "(5/10)". 2 more similar replacement(s)

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

          (75/100)*(x+20)-(2+(5/10)*(x-2))=0

           1

Simplify   —

           2

75             1

 (———•(x+20))-(2+(—•(x-2)))  = 0

  100             2

75                      (x - 2)

 (——— • (x + 20)) -  (2 +  ———————)  = 0

  100                         2  

3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  2  as the denominator :

         2     2 • 2

    2 =  —  =  —————

         1       2  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Answer: Answer: x=-56

Step-by-step explanation: Changes made to your input should not affect the solution:

(1): "0.5" was replaced by "(5/10)". 2 more similar replacement(s)

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

         (75/100)*(x+20)-(2+(5/10)*(x-2))=0

          1

Simplify   —

          2

75             1

(———•(x+20))-(2+(—•(x-2)))  = 0

 100             2

75                      (x - 2)

(——— • (x + 20)) -  (2 +  ———————)  = 0

 100                         2  

3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  2  as the denominator :

        2     2 • 2

   2 =  —  =  —————

        1       2  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Step-by-step explanation:

Answer:

its the first one and the last one ..that's the answer.

Answer:

4/15

Step-by-step explanation:

2/5 drive

1/3 bus

and rest walk

fraction of those who walk is 1-(2/5+1/3)

2/5+1/3=(6+5)/15=11/15

15/15-11/15=4/15

Answer:

Consider the parent logarithm function f(x) = log(x)

Now,

Let us make transformations in the function f(x) to get the function g(x)

•On streching the graph of f(x) = log(x) , vertically by a factor of 3, the graph of y = 3log(x) is obtained.

•Now, shrinking the graph of y = 3log(x) horizontally by a fctor of 2 to get the grpah of y = 3log(x/2) i.e the graph of g(x)

Hence, the function g(x) after the parent function f(x) = log(x) undergoes a vertical stretch by a factor of 3, and a horizontal shrink by a factor of 2 is

g(x) = 3 log(x/2) (Option-B).

Answer:

The answer is C.

as for C . the value of f(x) increases by 7 and so the graph goes up by units 7.

OR

g(x) = |x| + 7

we know that |x| is f(x), so :-

g(x) = f(x) + 7

and since f(x) is plot on y- axis the graph climbs the y axis by 7 units

*The graph shifts right or left for the other functions*

Answer:

D. 60.3

Step-by-step explanation:

Finding the mean,

M = (sum of values of data)/(number of data)

now, number of data = 9,

calculating the mean,

M = (54 + 68 + 68 + 54 + 59 + 58 + 68 + 57 + 57)/9

M = 543/9

M = 60.333

M = 60.3

Answer:

y=6

Step-by-step explanation:

x=3 is parallel to the y axis so the perpendicular line will be parallel to the x axis and will equals y=6 so it will pass through the point which have a y coordinate of 6

Answer:

20

Step-by-step explanation:

30% of 'something' equals 6.

Translated into math, that is

(.30)N = 6

N = 6/0.30

N = 20

The denominator is zero (0/0 is undefined), we cannot determine the exact value of f(-3) using this equation.

To solve the given equations, we need to find the value of the function f(x) for specific values of x.

"If f(x) / (x - 2) = x³ + 2x - 4 + 13/(x - 2), what is f(2)?"

To find f(2), we can substitute x = 2 into the equation and solve for f(2).

Plugging in x = 2, we get:

f(2) / (2 - 2) = 2³ + 2(2) - 4 + 13/(2 - 2)

Since the denominator is zero (2 - 2 = 0), the equation is undefined. Therefore, there is no solution for f(2) in this case.

"If f(x) / (x + 3) = 3x² - 4x + 2, what is f(-3)?"

To find f(-3), we can substitute x = -3 into the equation and solve for f(-3).

Plugging in x = -3, we get:

f(-3) / (-3 + 3) = 3(-3)² - 4(-3) + 2

Simplifying, we have:

f(-3) / 0 = 3(9) + 12 + 2

f(-3) / 0 = 27 + 12 + 2

f(-3) / 0 = 41

Additional information or context is needed to solve for f(-3).

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Answer:

Yes, dilation does not change the angle measurements.

Step-by-step explanation: